Question

Kinga Doll Company manufactures eight versions of its popular girl doll, Shari. The company operates on a 40-hour work week. The eight versions differ in doll skin, hair, and eye color, enabling most children to have a doll with a similar appearance to them. It currently sells an average of 4,000 dolls (spread equally among its eight versions) per week to boutique toy retailers.
In simplified terms, doll making at Kinga involves three basic operations: molding the body and hair, painting the face, and dressing the doll. Changing over between versions requires setup time at the molding and painting stations due to the different colors of plastic pellets, hair, and eye color paint required.
The table below lists the setup times for a batch and the processing times for each unit at each step. Unlimited space for buffer inventory exists between these steps. Assume that (i) setups need to be completed first, (ii) a setup can only start once the batch has arrived at the resource, and (iii) all flow units of a batch need to be processed at a resource before any of the units of the batch can be moved to the next resource.

a. What is the process capacity in units per hour with a batch size of 500 dolls?
b. What is the time it takes for the first batch of 500 dolls to go through an empty process?
c. Which batch size would minimize inventory without decreasing the process capacity?
d. Which batch size would minimize inventory without decreasing the current flow rate?